IIRC, in the manga was implied that only participants of the Plan can watch the transmissions, probably by means of a private stream video or a PPV system (it's almost sure that MBI owns the every TV broadcasting channel and ISP in the city). If that fails, there is also the Weirdness Censor. If an unrelated person happens to catch on the transmission, it's more likely they will think they are watching a particularly gory Supernatural Martial Arts show.
Of course, that still means that he just killed two young women on a live feed being viewed by his sister and mother (also his father, though he doesn't seem to care about the fact that he's still alive or his identity except in this case he is a Second Owner from Clocktower). And depending on when they started broadcasting, Miya may have also heard him admitting that he had attacked Karasuba with the plate he blamed her for stealing and may figure out that the damage to her floor was caused by that attack.
The story is a sequel to Fate, but in the epilogue we see it may also be a prequel to another work by Nasu, Angel Notes. The Black Aristoteles has just been sited on Jupiter, and Shirou and his flock are the first of the A-Rays. At best, this means Earth is fated to die and humanity will be on the verge of extinction. At worst, because only a handful of people were transformed into A-Rays by it being contained within the Reality Marble along with Shirou possibly being disinclined to pursue any further research in that line due to it being the work of his biological father, even the small amount of life persisting in that future won't survive.